Open AccessSOME FURTHER EXTENSIONS CONSIDERING DISCRETE PROPORTIONAL FRACTIONAL OPERATORS
Author(s) -
Saima Rashid,
Sobia Sultana,
Yeliz Karaca,
Aasma Khalid,
YuMing Chu
Publication year - 2021
Publication title -
fractals
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.654
H-Index - 44
eISSN - 1793-6543
pISSN - 0218-348X
DOI - 10.1142/s0218348x22400266
Subject(s) - uniqueness , mathematics , nabla symbol , operator (biology) , fractional calculus , type (biology) , kernel (algebra) , discrete time and continuous time , pure mathematics , mathematical analysis , statistics , omega , ecology , biochemistry , chemistry , physics , repressor , quantum mechanics , biology , transcription factor , gene
In this paper, some attempts have been devoted to investigating the dynamic features of discrete fractional calculus (DFC). To date, discrete fractional systems with complex dynamics have attracted the most consideration. By considering discrete [Formula: see text]-proportional fractional operator with nonlocal kernel, this study contributes to the major consequences of the certain novel versions of reverse Minkowski and related Hölder-type inequalities via discrete [Formula: see text]-proportional fractional sums, as presented. The proposed system has an intriguing feature not investigated in the literature so far, it is characterized by the nabla [Formula: see text] fractional sums. Novel special cases are reported with the intention of assessing the dynamics of the system, as well as to highlighting the several existing outcomes. In terms of applications, we can employ the derived consequences to investigate the existence and uniqueness of fractional difference equations underlying worth problems. Finally, the projected method is efficient in analyzing the complexity of the system.